Section 8: Conduit Systems Energy Losses

Energy grade line (EGL) computations begin at
the outfall and are worked upstream, taking each junction into consideration.
Many storm drain systems are designed to function in subcritical
flow. In subcritical flow, pipe and access hole losses are summed
to determine the upstream EGL. In supercritical flow, pipe and access
losses are not carried upstream.

Minor Energy Loss Attributions

Minor losses in a storm drain system are usually insignificant when
considered individually. In a large system, however, the combined
effects may be significant. The hydraulic loss potential of storm
drain system features, such as junctions, bends, manholes, and confluences,
can be minimized by careful design. For example, severe bends can
be replaced by gradual bends where right-of-way is sufficient and
increased costs are manageable. Well designed manholes and inlets without sharp
or sudden transitions or impediments to the flow cause no significant
losses.

Junction Loss Equation

A pipe junction is the connection of a lateral pipe to a larger
trunk pipe without the use of an access hole. The minor loss equation
for a pipe junction is in the form of the momentum equation. In Equation
10-36, the subscripts “i”, “o”, and “1” indicate the inlet, outlet,
and lateral, respectively.

The above assumes that the channel velocity is lower than
the outlet velocity. Note that, for partial flow, where the pipe
outfalls into a channel with water moving in the same direction,
the exit loss may be reduced to virtually zero.

In the outlet control condition, flow out of the access hole
is limited by the downstream storm drain system. The outflow pipe
would be in subcritical flow and could be either flowing full or partially
full.

Whether the outflow pipe is flowing full or partially full
affects the value of Eaio. This can be determined
by redescribing and rearranging the outflow pipe energy head, Ei.
Ei can be described as the sum of the potential
head, pressure head, and velocity head, as shown in Equation 10-40.

The revised access hole energy level (Ea)
is determined by adding three loss factors for: (1) benching configurations;
(2) flows entering the structure at an angle; and (3) plunging flows. Flows
entering a structure from an inlet can be treated as plunging flows.

Note that the value of Ha should always
be positive. If not, Ha should be set to
zero.

Additional Energy Loss: Benching

Benching serves to direct flow through the access hole, which
reduces energy losses. Figure 10-21 illustrates some typical bench
configurations. Department standard sheets do not show any benching
practices other than methods (a) and (b).

Figure 10-22 illustrates the orientation of the pipe inflow
angle measurement. The angle for each inflow pipe is referenced
to the outlet pipe, so that the angle is not greater than 180 degrees.
A straight pipe angle is 180 degrees. If all flows are plunging,
θw is set to 180 degrees; the angled inflow
coefficient approaches zero as θw approaches
180 degrees and the relative inflow approaches zero. The angled
inflow coefficient (Cθ) is calculated by
Equation 10-50:

As the proportion of plunging flows approaches zero, CP also
approaches zero.

Access Hole Energy Gradeline

Knowing the access hole energy level (Ea)
and assuming that the access hole flowline (Za)
is the same elevation as the outflow pipe flowline (Zi)
allows determination of the access hole energy gradeline (EGLa):

As described earlier, the potentially highly turbulent nature
of flow within the access hole makes determination of water depth
problematic. Research has shown that determining velocity head within
the access hole is very difficult, even in controlled laboratory
conditions. However, a reasonable assumption is to use the EGLa as
a comparison elevation to check for potential surcharging of the
system.

Inflow Pipe Exit Losses

The final step is to calculate the energy gradeline into each
inflow pipe, whether plunging or non-plunging.

Non-Plunging Inflow Pipe

Non-plunging inflow pipes are those pipes with a hydraulic
connection to the water in the access hole. Inflow pipes operating
under this condition are identified when the revised access hole
energy gradeline (Ea) is greater than the
inflow pipe flowline elevation (Zo). In this
case, the inflow pipe energy head (EGLo)
is equal to:

Exit loss is calculated in the traditional manner using the
inflow pipe velocity head since a condition of supercritical flow
is not a concern on the inflow pipe.

Plunging Inflow Pipe

For plunging inflow pipes, the inflow pipe energy gradeline
(EGLo) is logically independent of access
hole water depth and losses. Determining the energy gradeline for
the outlet of a pipe has already been described in
Chapter
6.

Continuing Computations Upstream

For either the nonplunging or plunging flows, the resulting
energy gradeline is used to continue computations upstream to the
next access hole. The procedure of estimating entrance losses, additional
losses, and exit losses is repeated at each access hole.

Energy Gradeline Procedure

Determine the EGLi and
HGLi downstream of the access hole. The EGL
and HGL will most likely need to be followed all the way from the
outfall. If the system is being connected to an existing storm drain,
the EGL and HGL will be that of the existing storm drain.

If HGLi is less
than the soffit of the outflow pipe but greater than critical depth
and less than or equal to normal depth, the pipe is in subcritical
partial flow. EGLi becomes the flowline elevation
plus normal depth plus the velocity head.

Determine the benching coefficient (CB)
using Table 10-4. Department standard sheets do not show any benching
practices other than depressed (a) or flat (b). The values are the
same whether the bench is submerged or unsubmerged.

Determine the plunging flow coefficient
(CP) for every pipe into the access hole
using Equation 10-52. The relative plunge height (hk)
is calculated using Equation 10-51. Zk is
the difference between the access hole flowline elevation and the
inflow pipe flowline elevation. If Zk > 10Do,
Zk should be set to 10Do.